Question

Graph the system of inequalities presented here on your own paper, then use your graph to answer the following questions:

y > 5x + 5
y is greater than negative 1 over 2 times x plus 1

Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)

Part B: Is the point (−2, 5) included in the solution area for the system? Justify your answer mathematically. (4 points)

Answer 1

disregard the inequality sign for now...
y > 5x + 5...we are going the find the x and y intercepts...x intercept can be found by subbing in 0 for y and solving for x...y intercept can be found by subbing in 0 for x and solving for y.
y = 5x + 5
y = 5(0) + 5
y = 5......so the y intercept is (0,5)

y = 5x + 5
0 = 5x + 5
-5x = 5
x = -1.....so the x intercept is (-1,0)

so plot ur points (0,5) and (-1,0)
Now look at the inequality we disregarded before...it is greater then...and it as no equal sign...because it has no equal sign, u will connect ur points with a dashed line...and since it is greater then, u will shade above the line.

do the same thing for the second inequality.

Is (-2,5) part of the solution ?
if u can sub in (-2,5)...x = -2 and y = 5 into BOTH inequalities and have them come out true, then it is part of the solution. Keep in mind, both inequalities have to be true, not just one, for it to be part of the solution.